Question

The National Center for Education Statistics reports the following statistics for surveys of 12,320 female college students and 9,184 male college students.

36% of females work 16-25 hours per week

38% of males work 16-25 hours per week

Suppose two students are selected with replacement. Find the probability that the first student is a female that works 16-25 hours per week and the second student is a female that works 16-25 hours per week. Round your answer to three decimal places.

Are the events dependent or independent?

Are the two events mutually exclusive? Event F: the subject is a female     Event G: the subject is a graduate student

Answer 1

Female students = n₁ = 12320

Male students = n₂ = 9184

Total students = 12320+9184 = 21504

1. Probability that the first student is a female that works 16-25 hours per week

= Probability a female student is selected*The female student works for 16-25 hours

= 0.206

2. Probability that the second student is a female that works 16-25 hours per week.

0.206

Explanation: Since two students are selected with replacement, the total number of stduents and female students does not change. Therefore, the probability does not change.

3.Are the events dependent or independent?

Yes the events are independent. As the trial is performed with replacement, the first event does not affect the second event.

Therefore

Where A =Probability that the first student is a female that works 16-25 hours per week

B = Probability that the second student is a female that works 16-25 hours per week

4. Are the two events mutually exclusive?

No, the events are not mutually exclusive.

Two events are mutually exclusive if event A and event B cannot occur together.

i.e.

But, . Therefore, they are not mutually exclusive.